There are three assets available to investors: 1) a stock fund with an expected
ID: 2800103 • Letter: T
Question
There are three assets available to investors: 1) a stock fund with an expected return of 1 7. 5% and a return standard deviation of 22% 2) a bond fund with an expected return of 7% and a return standard deviation of 10%, and 3) a risk-free asset with a return of 5 The correlation between the stock fund's return and the bond fund's return is 0. Mary is a risk-averse investor. Answer the following questions %. a. If Mary invests 3% of her portfolio wealth in the stock fund and 97% in the bond fund (She invests nothing in the risk-free asset), what is the expected return and standard deviation of her portfolio? [1 pt) b. If Mary invests 100% of her portfolio wealth in the bond fund, what is the expected return and standard deviation of her portfolio? [1 pt] c. Which portfolio between a) and b) would Mary prefer? Explain your answer. [I pt)Explanation / Answer
Portfolio Returns = wA x (RA) + wB x (RB)
Portfolio standard deviation = square root [w2A x 2(RA) + w2B x 2(RB) + 2x (wA)x (wB)x Cov(RA, RB)]
since covariance of bond and stock is zero, formula will reduce as
Portfolio standard deviation = square root [w2A x 2(RA) + w2B x 2(RB)]
Using above formulas:
a Portfolio Returns = 3%x15%+97%x7% = 7.24%
Portfolio standard deviation = square root [0.032x 0.222 + 0.972x 0.102]
= square root [0.009453]
=9.72%
b Portfolio Returns = 7%
Portfolio standard deviation = 10%
c risk adjusted returns of portfolio a = 7.24% / 9.72% = 0.745%
risk adjusted returns of portfolio b = 7% / 10% = 0.7%
Therefore portfolio a is better since risk adjusted returns of portfolio a are better
d Mary will combine the portfolio with stock portfolio since stocks provides asset class diversification. Bond Portfolio and risk free bonds are same asset class and thus less diversification benefits. Thus risk-adjusted returns with stock portfolio will be higher.
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